GENERALIZATION OF CERTAIN RESULTS ON PROJECTIVE MOTION IN A FINSLER SPACE
Abstract
Abstract: The paper contains a study of an infinitesimal projective motion in a Finsler space Fn(n > 2), which leaves invariant the skew- symmetric part of the covariant
derivative of projective deviation tensor and it is proved that either the Finsler space Fn(n > 2) admitting such projective motion is a space of scalar curvature or the infinitesimal projective motion is necessarily an affine motion. It is established that an infinitesimal projective motion in a projectively flat as well as in a non- Riemannian symmetric Finsler space of dimension greater than 2, is necessarily an
affine motion while a symmetric Finsler space Fn(n > 2) admitting a non- affine projective motion is a Riemannian space of constant Riemannian curvature. An infinitesimal projective motion in a Finsler space Fn(n > 2) of recurrent projective deviation tensor is an affine motion if the projective motion leaves invariant the recurrence vector of the space. It is further proved that such result also holds in case of projective recurrent and recurrent Finsler space of dimension greater than 2.
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K. Yano and T. Nagano, Some theorems on projective and conformal transformations, Nederl. Akad. Wetensch. Proc. Ser. A. 60= Indag. Math., 19 (1957), 451-458.
P. N. Pandey, Projective motion in a symmetric and projectively symmetric Finsler manifold , Proc. Nat. Acad. Sci., 54(A) (1984) 274-278.
H. Rund, The differential Geometry of Finsler spaces, Springer- Verlag, (1959).
R. B. Misra, A projective symmetric Finsler space, Math. Z., 126 (1972), 143-153.
P. N. Pandey, A note on recurrence vector, Proc. Nat. Acad. Sci., 50 (A) (1980), 6-8.
Z. I. Szabo, Ein Finslerscher Raum ist gerade dann von skalarer Kr¨ummung, wenn seine Weylsche Projektivkr¨ummung verschwindet, Acta Sci. Math. Szeged, 39 (1977), 163-168.
P. N. Pandey, On a Finsler space of zero projective curvature,Acta. Math. acad. Sci. Hungar, 39(4)(1982), 387-388.
P. N. Pandey, On Some Finsler spaces of scalar curvature, Prog. of Maths., 18(1) (1984), 41-48.
P. N. Pandey and R. B. Misra , Projective recurrent Finsler manifolds I , Publications Mathematicae Debrecen, 28(3-4)(1981),191-198.
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